ASA calculation for CsPbI3 in cubic and pseudocubic structures

The energy band structure of CsPbI3 is computed in both an ideal cubic structure, and also a pseudocubic structure, using the LDA code lmf.

Corresponding calculations are carried out using the ASA code lm, and results compared.

A QSGW calculation is carried out, which modifies the band structure and widens the bandgap.

This tutorial is self-contained. It is required to prepare necessary inputs to the Levenberg-Marquardt tutorial which makes small adjustments to the ASA potential parameters to fit the ASA bands to QSGW bands.

Introduction

CsPbI3 is a close cousin of NH3CH3PbI3 (usually called MAPI). They are in the family of perovskites that have attracted a great deal of attention recently because of their considerable potential as efficient, low-cost solar cells.

CsPbI3 has, on average, a cubic structure. However, the PbI3 cage flexes rather dramatically in time, roughly on the scale of a phonon period, distorting the underlying cubic structure and changing the instantaneous band structure. MAPI flexes in a similar way, but CsPbI3 is simpler so this tutorial is written for it. The effect of distortions on the band structure is significant, and it is the subject of this tutorial. It is based on a paper analyzing the effects of nuclear motion in CHNHPbI and CsPbI.

This tutorial develops the energy bands for CsPbI3 in its ideal cubic structure, and a pseudocubic structure which approximates the flexing of the system at room temperature.

LDA-ASA energy bands, calculated with lm

The ASA doesn’t have a Mattheis construction to supply a reasonable starting guess the charge density, as lmf does. On the other hand, because it is the ASA, it is able to store information about the density in a highly compact way1.

Extract l resolved sphere charges generated by lmf

The ASA contracts all the information about the density into energy moments of the sphere charges 1, for each l. This step is not necessary, but it makes use of moments generated by lmf as input to the ASA. Thus it supplies a reasonable starting guess for the density.

The flat state at 3 eV is bright red, showing that is of Pb character. You can make further use of the color weights to establish that it is a Pb d state (we won’t do that here).

Self-consistent ASA

The spurious state or “ghost band,” 2 must be removed before proceeding. In this particular instance the problem can be fixed simply by reducing the overlap between the Pb and empty spheres. But this is a special case. For pedagogical reasons, we point out three other ways to solve the problem.

Downfold the Pb 6d.

Freeze the Pb 6dcontinuous principal quantum numberPd at a higher value than the one reached through the self-consistency cycle 2 (PMIN=-1 is designed to guard against this problem but it wasn’t sufficient.)

Replace P on the Pb with 5d. So far we have treated the Pb 5d as a core state. This will improve the treateent of the the Pb 5d, but in the region of the Fermi level, Pb has more 6d than 5d character near the Fermi level, so we might expect this method to be a little less accurate.

In setting up the starting conditions the Pb moments are now completely out of whack, since Pb 6d and Pb 5d are very different. Rather than try to guess Pb moments, instead we can remove the Pb atom file, let lm choose some moments taken from the free atom, and scale the charge on that atom to enforce charge neutrality.

Bands no longer have a spurious state at 3 eV, and they are in reasonable agreement with the full LDA result.

Pseudocubic structure

Compare site0.dcspbi and site0.cspbi. They are basically the same structure, with relatively modest distortions, but:

alat and plat are distributed differently: plat(i,i) is about 6.2, corresponding to the (slightly distorted) cube edge in Angstroms. This data was extracted from a VASP POSCAR file.

Some sites are translated by approximate integer multiples of lattice vectors (approximate because of distortions)

The order of the Iodine sites is permuted.

It is convenient to render the site file of the distorted lattice as near as possible to the undistorted one. Then comparisons are simpler to make. A combination of switches in the blm and lmscell make this easy work.

LDA energy bands, pseudocubic structure

blm can eliminate difference (1) with the --scala switch, and most of the differences in lattice translations elminated with the --xshft switch.

site1.dfp and site.fp are much closer to each other. The superlattice editorlmscell --stack can undo the permutation of Iodine sites with the ~sort option, and it can clean the up the one remaining difference in the translation vector (Cs) with the ~addpos option.

If no data is available for a particular atom, the ASA codes lm, lmgf, and lmpg select from charges in the atom, and sets to zero. It reads preset values for the and from a lookup table. This is will make a crude estimate of the density, but it is usually sufficient to make a starting guess, which can be iterated to the self-consistent values.

Another alternative is to extract the moments from the same species of a different self-consistent calculation, as a starting guess for the self-consistent moments.

A third alternative is to extract the moments , and boundary conditions , from a full-potential calculation run by lmf. The present tutorial follows this strategy.

2 Normally the continuous principal quantum numbers. are allowed to float to band center of gravity (the at which vanishes), but when the partial wave is far removed from the Fermi level, this can cause “ghost bands” to appear. One guard against this is to restrict the , and not let it fall below the free-electron value. Tag HAM_PMIN is designed for this purpose. Another guard is to freeze the to a fixed value, using SPEC_ATOM_IDMOD. Another way is to downfold the . You can tell the ASA codes to downfold a particular state with SPEC_ATOM_IDXDN.

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